Finite volume chiral partition functions and the replica method

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In the framework of chiral perturbation theory we demonstrate the equivalence of the supersymmetric and the replica methods in the symmetry breaking classes of Dyson indices [Formula Presented] and [Formula Presented] Schwinger-Dyson equations are used to derive a universal differential equation for the finite volume partition function in sectors of fixed topological charge, [Formula Presented] All dependence on the symmetry breaking class enters through the Dyson index [Formula Presented] We utilize this differential equation to obtain Virasoro constraints in the small mass expansion for all [Formula Presented] and in the large mass expansion for [Formula Presented] with arbitrary [Formula Presented] Using quenched chiral perturbation theory we calculate the first finite volume correction to the chiral condensate demonstrating how, for all [Formula Presented] there exists a region in which the two expansion schemes of quenched finite volume chiral perturbation theory overlap. © 2003 The American Physical Society.
Original languageEnglish
JournalPhysical Review D
Issue number12
Publication statusPublished - 1 Jan 2003

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